If you're new to Gene Kelly, I'd recommend you begin with Clive Hirschhorn's biography and Besty Blair's memoir (Blair was married to Kelly for 16 years).
On GEne Kelly
- Basinger, Jeanine. Gene Kelly (Illustrated History of the Movies). TBS The Book Service Ltd., 1978.
- Blair, Betsy. The Memory of All That: Love and Politics in New York, Hollywood, and Paris. New York: Alfred A. Knopf, 2003.
- Brideson, Cynthia and Sara Brideson. He's Got Rhythm: The Life and Career of Gene Kelly. University Press of Kentucky, 2017.
- Hirschhorn, Clive. Gene Kelly: A Biography. Chicago: Regnery, 1975.
- Masson, Alain. Gene Kelly. Paris: Gallimard, 2012. [in French]
- Morley, Sheridan. Gene Kelly: A Celebration. Oxfordshire: Pavillion, 1997.
- Yudkoff, Alvin. Gene Kelly: A Life of Dance and Dreams. New York: Back Stage Books, 1999.
on Gene Kelly's Films
- Casper, Joseph Andrew. Vincente Minnelli and the Film Musical (1977).
- Fordin, Hugh. MGM's Greatest Musicals: The Freed Unit. New York: Da Capo Press, 1975.
- Hess, Earl J. and Pratibha A. Dabholkar, The Cinematic Voyage of The Pirate: Kelly, Garland, and Minnelli at Work. UP Missouri, 2014.
- Hess, Earl J. and Pratibha A. Dabholkar, Singin’ in the Rain: The Making of an American Masterpiece” UP Kansas, 2009.
- Knox, Donald. Magic Factory, The: How MGM Made An American in Paris (1973).
- Sylvester, Stephen X. and Michael Troyan. MGM: Hollywood's Greatest Backlot (2011).
- Thomas, Tony. The Films of Gene Kelly, Song and Dance Man. Secaucus, N.J., Citadel Press, 1974.
- Silverman, Stephen M., Dancing on the Ceiling: Stanley Donen and His Movies. New York: Knopf, 1996.
- Wollen, Peter. Singin' in the Rain. London: BFI Publishing, 1992.